ACTION AND REACTION. 



201 



ing parts of A's motion being equally distributed between them. Each body- 

 will, therefore, have two parts of A's original motion, and 2 therefore will be 

 their common velocity after impact. In this case, A loses 8 of the 10 parts of 

 its motion in the direction A C. On the other hand, B loses the entire of its 6 

 parts of motion in the direction B C, and receives 2 parts in the direction A C. 

 This is equivalent to receiving 8 parts of A's motion in the direction A C. Thus, 

 according to the law of " action and reaction," B receives exactly what A loses. 



Finally, suppose that both the masses and velocities of A and B are unequal. 

 Let the mass of A be 8, and its velocity 9 ; and let the mass of B be 6, and its 

 velocity 5. The quantity of motion of A will be 72, and that of B, in the oppo- 

 site direction, will be -30. Of the 72 parts of motion which A has in the direc- 

 tion A C, 30, being transferred to B, will destroy all its 30 parts of motion in 

 the direction B C, and the two masses will move in the direction C B, with 

 the remaining 42 parts of motion, which will be equally distributed among their 

 14 component masses. Each component part will, therefore, receive three 

 parts of motion ; and accordingly 3 will be the common velocity of the united 

 mass after impact. 



When two masses, moving in opposite directions, impinge and move together, 

 their common velocity after impact may be found by the following rule : " Mul- 

 tiply the numbers expressing the masses by those which express the velocities 

 respectively, and subtract the lesser product from the greater ; divide the re- 

 mainder by the sum of the numbers expressing the masses, and the quotient 

 will be the common velocity ; the direction will be that of the mass which has 

 the greater quantity of motion." 



It may be shown, without difficulty, that the example which we have just 

 given obeys the law of " action and reaction." 



Before impact. 

 Mass of A 8 



Velocity of A 9 



Quantity motion in direction AC 8X9 or 72 



Mass of B 6 



Velocity of B 5 



Quantity motion in direction B C 6X5 or 30 



After impact. 

 Mass of A 8 



Common velocity 3 



Quantitymotion in direction AC 8X3 or 24 



Mass of B 6 



Common velocity 3 



Quantity motion in direction A C 6X3 or 18 



Hence it appears that the quantity of motion in the direction A C, of which A 

 has been deprived by the impact, is 48, the difference between 72 and 24. On 

 the other hand, B loses by the impact the quantity 30 in the direction B C, 

 which is equivalent to receiving 30 in the direction A C. But it also acquires 

 a quantity 18 in the direction A C, which, added to the former 30, gives a total 

 of 48 received by B in the direction A C. Thus the same quantity of motion 

 which A loses in the direction A C, is received by B in the same direction. 

 The law of " action and reaction" is, therefore, fulfilled. 



The examples of the equality of action and reaction in the collision of bodies 

 may be exhibited experimentally by a very simple apparatus. Let A and B, 

 fig. 2, be two balls of soft clay, or any other substance which is inelastic, or 

 nearly so, and let these be suspended from C by equal strings, so that they may 

 be in contact ; and let a graduated arch, of which the centre is C, be placed so 

 that the balls may oscillate over it. One of the balls being moved from its 

 place of rest along the arch, and allowed to descend upon the other through a 

 certain number of degrees, will strike the other with a velocity corresponding 

 to that number of degrees, and both balls will then move together with a velo- 

 city which may be estimated by the number of degrees of the arch through 

 which they rise. 



In all these cases in which we have explained the law of " action and reac- 



